Satellite-based positioning systems include constellations of earth orbiting satellites that constantly transmit orbit information and ranging signals to receivers. An example of a satellite-based positioning system is the Global Positioning System (GPS), with its constellation of GPS satellites. Orbit information and ranging signals transmitted by the GPS satellites are received by GPS receivers. To determine its position, a GPS receiver acquires and tracks satellite signals from three or more GPS satellites to measure a range from the GPS receiver to each satellite and to demodulate the transmitted orbit information. Transmissions of GPS satellite signals are modulated by a satellite-specific 1023-chip pseudo-random number (PRN) code that is repeated every millisecond. Transmissions of satellite signals from all GPS satellites are also synchronized. At the GPS receiver, a code phase of the satellite signal is received with a delay corresponding to the time it takes for the satellite signal to travel from the satellite to the receiver. By measuring the delays in the code phase to three or more satellites and by knowing the positions of the satellites, the GPS receiver is able to determine its position. The received satellite signal is also frequency shifted by a Doppler frequency due to the relative motion between the satellite and the GPS receiver and also due to a receiver oscillator error. The GPS receiver acquires a satellite by searching for the satellite's PRN code in a two-dimensional search space divided into multiple code phase/Doppler frequency test hypotheses.
In a conventional acquisition process, one correlation resource is allocated to each code phase/Doppler frequency hypothesis. The correlation resource integrates the cross-correlation energy of the hypotheses with the received satellite signal. Cross-correlation using the correlation resources continues until one of the cross-correlation energies exceeds a threshold which indicates that the signal has been detected using the corresponding hypothesis. Generally, a satellite signal with a low signal level requires long non-coherent integration time for reliable detection. However, long non-coherent integration time may present a problem. For example, when there is an uncompensated receiver clock frequency rate, the apparent Doppler frequency of the received satellite signal may change during the long non-coherent integration time, causing the satellite signal to move across hypotheses. The cross correlation energy may then be degraded, resulting in an increased probability of missed detection. In addition, where there are a large number of hypotheses used to search for signals in a large search space, long non-coherent integration time may result in expenditure of significant energy, leading to reduced battery life. Therefore, it is desirable to find ways to reduce the number of hypotheses, especially when acquiring satellite signal with low signal levels.